On Ising model with four competing interactions on Cayley tree - Ganikhodjaev, Nasir; Rozikov, Utkir Abdulloevich (Springer Netherlands, 2009)
In the paper we consider an Ising model with four competing interactions (external field, nearest neighbor, second neighbors and triples of neighbors) on the Cayley tree of order two.We show that for some parameter values of the model there is a phase transition. Our second result gives complete description of the periodic Gibbs measures for the model. We also construct uncountably many non-periodic extreme Gibbs measures.